What is the solution for y^{'''}-3y^{''}-25y^'-21y=0 ?

The solution for y^{'''}-3y^{''}-25y^'-21y=0 is y=c_{1}e^{-t}+c_{2}e^{-3t}+c_{3}e^{7t}

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y^{'''}-3y^{''}-25y^'-21y=0

y^{^{'''}} - 3 y^{^{''}} - 25 y^{^{'}} - 21 y = 0

y = c_{1} e^{- t} + c_{2} e^{- 3 t} + c_{3} e^{7 t}

Solution steps

y^{'''} (t) - 3 y^{''} (t) - 25 y^{'} (t) - 21 y = 0

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{- 3 t} + c_{3} e^{7 t}

y = c_{1} e^{- t} + c_{2} e^{- 3 t} + c_{3} e^{7 t}

0.5 y^{^{''}} + 6 y^{^{'}} + 50 y = 0

y^{^{''}} + 2 y^{^{'}} + 2 y = 0, y (0) = 1, y^{^{'}} (0) = 1

\frac{d ^{3} y}{d x ^{3}} = \frac{d y}{d x}

16 y^{^{''''}} = 625 y

y^{^{''}} + 64 y = 0, y (0) = \frac{2}{3}, y^{^{'}} (0) = - \frac{4}{3}

What is the solution for y^{'''}-3y^{''}-25y^'-21y=0 ?
The solution for y^{'''}-3y^{''}-25y^'-21y=0 is y=c_{1}e^{-t}+c_{2}e^{-3t}+c_{3}e^{7t}